Related papers: Shrinking parallelepiped targets in beta-dynamical…

Let $P$ be a polytope defined by the system $A x \leq b$, where $A \in R^{m \times n}$, $b \in R^m$, and $\text{rank}(A) = n$. We give a short geometric proof of the following tight upper bound on the number of vertices of $P$: $$ n! \cdot…

Radio frequency (RF) wireless power transfer (WPT) is a key technology for future low-power wireless systems. However, the inherently low end-to-end power transfer efficiency (PTE) is challenging for practical applications. The main factors…

A fundamental challenge within the metric theory of continued fractions involves quantifying sets of real numbers, when represented using continued fractions, exhibit partial quotients that grow at specific rates. For any positive function…

Radio frequency wireless power transfer (WPT) enables charging low-power mobile devices without relying on wired infrastructure. Current existing WPT systems are typically designed assuming far-field propagation, where the radiated energy…

This article is the first one in a series of two dealing with the concept of "resonant metalens" we recently introduced [Phys. Rev. Lett. 104, 203901 (2010)]. Here, we focus on the physics of a medium with finite dimensions consisting on a…

We introduce the notions of directional dynamical cubes and directional regionally proximal relation defined via these cubes for a minimal $\mathbb{Z}^d$-system $(X,T_1,\ldots,T_d)$. We study the structural properties of systems that…

For a hyperplane $H$ supporting a convex body $C$ in the hyperbolic space $\mathbb{H}^d$ we define the width of $C$ determined by $H$ as the distance between $H$ and a most distant ultraparallel hyperplane supporting $C$. The minimum width…

Let $P$ be a set of $n$ points in $\Re^2$. For a parameter $\varepsilon\in (0,1)$, a subset $C\subseteq P$ is an \emph{$\varepsilon$-kernel} of $P$ if the projection of the convex hull of $C$ approximates that of $P$ within…

We study the replacement paths problem in the $\mathsf{CONGEST}$ model of distributed computing. Given an $s$-$t$ shortest path $P$, the goal is to compute, for every edge $e$ in $P$, the shortest-path distance from $s$ to $t$ avoiding $e$.…

Retroreflectors that can accurately redirect the incident wave in free space back along its original channel provide unprecedented opportunities for light manipulation in wireless communication. However, to the best of our knowledge, the…

We show optimal triangulations for piecewise linear (PWL) approximations of indefinite quadratic functions over the plane. Optimal triangulations have minimum triangle density while allowing a PWL approximation that fulfills a prescribed…

For any $\beta > 1$, let $T_\beta: [0,1)\rightarrow [0,1)$ be the $\beta$-transformation defined by $T_\beta x=\beta x \mod 1$. We study the uniform recurrence properties of the orbit of a point under the $\beta$-transformation to the point…

In this paper, we investigate inhomogeneous and simultaneous Diophantine approximation in beta dynamical systems. For $\beta>1$ let $T_{\beta}$ be the $\beta$-transformation on $[0,1]$. We determine the Lebesgue measure and Hausdorff…

We propose a distributionally robust approach to learning hyperparameters for first-order methods in convex optimization. Given a dataset of problem instances, we minimize a Wasserstein distributionally robust version of the performance…

In this paper, we investigate the Hausdorff measure of shrinking target sets in $\beta$-dynamical systems. These sets are dynamically defined in analogy to the classical theory of weighted and multiplicative approximation. While the…

For an $n$-vertex digraph $G=(V,E)$, a \emph{shortcut set} is a (small) subset of edges $H$ taken from the transitive closure of $G$ that, when added to $G$ guarantees that the diameter of $G \cup H$ is small. Shortcut sets, introduced by…

The retrodirective antenna array is considered as a mechanism to enable target tracking of a power receiver for long range wireless power transfer (WPT) due to its simplicity in implementation using only analog circuits. By installing the…

Wireless Power Transfer (WPT) is expected to be a technology reshaping the landscape of low-power applications such as the Internet of Things, Radio Frequency identification (RFID) networks, etc. Although there has been some progress…

Let $T_\beta$ be the $\beta$-transformation on $[0,1)$ defined by $$T_\beta(x)=\beta x\text{ mod }1.$$ We study the Diophantine approximation of the orbit of a point $x$ under $T_\beta$. Precisely, for given two positive functions…

The SetCover problem has been extensively studied in many different models of computation, including parallel and distributed settings. From an approximation point of view, there are two standard guarantees: an $O(\log…